The invention relates to a process for the registration of two different images of the same object and in particular two multimode images. It has applications in all fields requiring a superimposing of different images of the same object and particularly in the fields of non-destructive testing and medical imaging.
The exploitation of images often requires a superimposing thereof. Although these images generally represent the same object, they are not directly superimposable for different reasons, namely they can be taken at different times or using different acquisition systems.
In addition, even for images having equivalent geometrical structures (i.e. images containing elements of identical objects), the distribution of the grey levels on the two images to be superimposed can differ between individual images and reference is then made to multimode images.
In order to be simultaneously exploitable and in particular superimposable, such images must be brought into correspondence beforehand, i.e. brought into a geometrical reference marking common to both images. It is consequently necessary to determine the geometrical transformation making it possible to represent one of the images in the geometrical reference marking of the other image and this is called image registration.
In particular, image registration is necessary in medical imaging in order to permit the observation of the same part of the human body from which an image has been obtained, e.g. by a X-radiation scanner and another image is obtained e.g. by magnetic resonance imaging (MRI) or by single photon emission tomography (SPECT).
FIGS. 1A and 1B show two examples of images of a human brain. FIG. 1A shows an axial section of the brain in MRI and FIG. 1B an axial section of the brain in SPECT. These two images, with different scopes, are linked by a rigid transformation.
At present, several methods are known for the registration of two images of the aforementioned type.
Certain methods make the hypothesis that the grey level distributions are equivalent for the registration of the two images. The grey levels of the images are then directly used for calculating the off-set between the two images. Among these methods there is the intercorrelation method consisting of determining the maximum of a function of the transformation or a product in the frequency range.
However, these methods suffer from a major disadvantage, which is the fact that the noise in the images and certain local distortions can hide the correlation peak, which falsifies the results of the registration.
Moreover, as a result of the actual hypothesis made on the grey levels, these methods cannot be used for multimode images.
Certain of these registration methods are based on space or frequency moments of the images and make it possible to determine the location, orientation or change of size of an object in an image. However, even if in theory an image is completely described by all its moments, in practice the high order moments are very sensitive to noise and contour distortions.
In the case where the images are very noisy or the grey levels of the images differ excessively, or if the images are in different scopes, the registration algorithm of these methods is falsified and the registration of the images is incorrect.
Other registration methods are also known. These methods use a higher order information based on visual marks extracted from the images. For example, certain of these methods consist of isolating, in both images, points in direct correspondence. These points are either selected manually in each of the two images, or are selected by means of markers designating, prior to acquisition, certain reference points on the basis of which the images will be registered. The distance between these points is then progressively decreased by a registration algorithm based e.g. on a least squares regression, on a breaking down into 3D eigenvalues, or other known, mathematical methods. These methods can be used for contours, surfaces or any other group of points.
They have the advantage of permitting the handling of a reduced information quantity compared with that of the previously described methods, whilst still taking account of the introduction of a higher information. However, they suffer from the disadvantage of being dependent on the way in which the informations are revealed.
Moreover, the informations extracted from the two images must necessarily represent the same structures (elements of objects contained in images), particularly for multimode images. These methods can then be unstable with respect to modifications in the extracted informations, which leads to geometrical errors.
In particular, for acquired images (i.e. non-simulated), the extraction of informations is generally unstable and difficult, a change of parametrizing may completely change the solution found. For example, a threshold change in most cases modifies the structure of the object extracted from the image.
Another known method is the phase translation registration method, which is deduced from the Fourier transform properties with respect to the translation in the space range (DIGITAL IMAGE PROCESSING, W. K. PRATT, Ed. Wiley Interscience, p 12). In this method, u({right arrow over (x)}) and v({right arrow over (x)}) are respectively the two images considered, where {right arrow over (x)} is the vector of the coordinates. If the two images are linked by a translation of vector {right arrow over (t)}, we obtain:
u({right arrow over (x)})=v({right arrow over (x)}xe2x88x92{right arrow over (t)}).
By Fourier transform, where f represents the space coordinates, we then obtain:
U({right arrow over (f)})=|U({right arrow over (f)})|xc2x7ejxcex8u({right arrow over (f)})=|V({right arrow over (f)})|xc2x7ejxcex8u({right arrow over (f)})xc2x7ej({right arrow over (t)}.{right arrow over (f)})=V({right arrow over (f)})xc3x97eJ({right arrow over (f)}.{right arrow over (f)})
Whilst only retaining the phases of the signals and forming their product are conjugacy of one of them, and taking the inverse transformation, we obtain:
Jxe2x88x921(ej(xe2x88x92xcex8u({right arrow over (f)})+xcex8u({right arrow over (f)})+{right arrow over (t)}.{right arrow over (f)}))=Jxe2x88x921(ej({right arrow over (t)}.{right arrow over (f)}))=S{right arrow over (t)}({right arrow over (x)}).
It is then possible to observe a Dirac peak at {right arrow over (x)}={right arrow over (t)}.
However, this method is firstly limited to images with the same scopes and then to translation-type transformations.
A method based on maximization of mutual information permits a registration of multimode images. Such a method is described in the document xe2x80x9cMultimodality Image Registration by Maximization of Mutual Informationxe2x80x9d by MAES, CALLIGNON et al, IEEE Transactions on Medical Imaging, vol. April 16, 1997 or in the document xe2x80x9cMulti-modal volume registration by maximization of mutual informationxe2x80x9d, by WELLS et al, Medical Image Analysis, vol. 1, No. 1, pp 35-51, February 1996.
This method suffers from the disadvantage of requiring a large number of calculations, as well as an optimization algorithm in order to converge towards the solution, which leads to problems of non-constant calculating times and a risk of convergence towards a local minimum, which corresponds to a poor solution.
The object of the invention is to obviate the disadvantages of the previously described methods. It therefore proposes a process for the registration, in a quasi-constant time, of two different images, which can be multimode images. This method consists of breaking down each of the images into space components representing the distribution of the grey levels of the image, applying the phase registration method to the components for bringing about correspondence of the components of one image with those of the other image, summating all the results of the bringing into correspondence and detecting, in the image resulting from said summation, the maximum grey level defining the transformation between the two initial images.
More specifically, the invention relates to a process for determining a geometrical transformation between two different images I1 and I2, both representative of the same object, with a view to the superimposing thereof. This process is characterized in that it consists of:
E13) segmenting each of the images into different components and deducing therefrom for each image, a group of segmented images,
E16) registering the thresholded images by a phase-based bringing into correspondence of each image:
16a) by taking, in the group of thresholded images corresponding to the image I1 and in the group of thresholded images corresponding to the image I2, respectively, a first and a second thresholded image components constituting the first and second components of a pair of components,
16b) carrying out a transform T for passing each component of the pair of the space range to a dual frequency range,
16c) calculating a phase image for each component of the pair,
16d) calculating, for each pair, a difference between the two phase images of the two components of the pair and deducing therefrom a phase difference image,
16e) determining the inverse transform Txe2x88x921 of the transform T of said phase difference image for determining an offset image and
16f) performing the stages 16a to 16e for each pair of components,
E18) summating all the offset images obtained in 16e for determining a total offset image and
E20) determining, in each total offset image, the pixel having the maximum value, the coordinates of said pixel fixing the parameters of the geometrical transformation between the two images I1 and I2.
According to a first embodiment of the invention, in which the geometrical transformation is a translation, stages 16b to 16e consist of applying an elementary Fourier transform.
According to a second embodiment of the invention, where the geometrical transformation is a rotation associated with a scale change, the stages 16b and 16e consist of applying the Fourier-Mellin transform to a group constituted by a rotation and a scale change and associating it with a Haar measure for determining the parameters of the rotation and the scale change.
According to a third embodiment of the invention, in which the geometrical transformation is a translation associated with a rotation, the stages 16b to 16e consist of applying an elementary Fourier transform associated with a rotation of the images.
In this embodiment:
successive registrations are applied to the two images carrying out successive rotations on one of the two images and mutually registering the same on each occasion by the translation phase method (cf. first embodiment),
an offset image is determined for one translation and for each registration,
the maximum value pixel in the group of offset images obtained for all the rotations is sought (the translation is determined by the position of the maximum pixel of the image containing it), the offset image containing this maximum being associated with a rotation, said rotation and the translation defining the geometrical transformation.
Advantageously, the process according to the invention consists of extending the phase difference images by a zero-padding method in order to increase the precision of the parameters determined in stage E20.
According to an embodiment of the invention, the segmentation E13 of the images takes place as a function of the grey levels of the images, said segmentation consisting of:
E12) determining, for each image, a histogram of the grey levels of the image and choosing, among said grey levels, n grey level thresholds for each image, with n greater than 2,
E14) breaking down each of the images as a function of its n grey level thresholds and deducing therefrom, for each image I1 and I2, a group of nxe2x88x921 segmented images.